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Invariant Markov semigroups on quantum homogeneous spaces

2019

Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …

Pure mathematicsAlgebra and Number TheoryLaplace transformMarkov chainMathematics::Operator AlgebrasProbability (math.PR)[MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA]Mathematics - Operator Algebras46L53 17B37 17B81 46L65 60B15 60G51 81R50Invariant (physics)[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]ConvolutionFOS: MathematicsGeometry and TopologyCompact quantum groupOperator Algebras (math.OA)QuantumLaplace operatorMathematical PhysicsEigenvalues and eigenvectorsMathematics - ProbabilityMathematics
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